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Questions

Non-normal distribution models are used more and more in order to price financial assets. We provide some basic questions and their respective answers on non-normal distributions:

(1) What is the distribution skewness when you see more returns on the left of the mean?
a) Skewness>0
b) Skewness<0
c) Skewness=0

(2) What is the probability of having a return lower than -2.33 standard deviations?
a) 5%
b) 2%
c) 1%

(3) What is the kurtosis of a normal distribution ?
a) 3
b) 0
c) -3

(4) Which is the less dangerous for a risk averse investor?
a) Positive skewness with kurtosis>3
b) Negative skewness with kurtosis>3
c) Negative skewness with kurtosis<3

(5) Assume a normally distributed fund with an historical annualized return of 10% and an annualized volatility of 5%.  How many years should you wait in order to have a monthly return of -5%?
a) 37 years
b) 137 years
c) 3137 years

(6) Assume you invested in the 3 best S&P500 monthly returns and you have shorted the 3 worst S&P500 monthly returns, since 1990. What is this 6 dates cumulative return?

a) 50%
b) 98%
c) 198%

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Answers

(1) Skewness>0
(2) 1%
(3) 3
(4) Positive skewness with kurtosis>3
(5) 2822 years (i.e. [1 / normdist(-5%, (1+10%)^(1/12)-1,5%/12^0.5,1)] / 12 )
(6) 98%. This means you made 98% in 6 months.